BFMFES C04L0102 Q1

A boundary layer is a thin region (usually along a wall) in which viscous forces are significant and within which the flow is rotational. Consider a boundary layer that grows along a thin flat plate. The flow is steady. The thickness of the boundary layer δ at any downstream distance x is a function of x, the free-stream velocity V∞, and the fluid properties ρ (density) and µ (viscosity). Use the method of repeating variables to generate a dimensionless relationship for δ as a function of the other parameters.

Water at 20°C flows through a long, straight pipe. The pressure drop is measured along a section of the pipe of length L = 1.3 m as a function of the average velocity V through the pipe (Table). The inner diameter of the pipe is D = 10.4 cm.

1. Find the Reynolds Number and the Euler number at highest speed.
2. Extrapolate the experimental data to predict the pressure drop at an average velocity of 80 m/s.